We use piecewise polynomials of time to parameterize the UAV trajectories. Due to the differential flatness of quadrotor dynamics [1]}, it is sufficient to characterize the trajectories as a smooth curve in the space of flat outputs \(\sigma : [t_0,t_m] \rightarrow \mathbb {R}^3 \times SO(2)\)  as \(\sigma (t) = [x(t),y(t),z(t),\psi (t)]^\top \) , which contains the coordinates of the vehicle's center of mass in the world coordinate system \(r = [x,y,z]^\top \)  and yaw angle \(\psi \) . Consider \(m\)  piecewise polynomials that characterize the entire trajectory, where each piece is an \(n\) -th order polynomial, i.e., for \(i \in \lbrace 1,2,\dots ,m \rbrace \) ,
\(\sigma _i(t) = \sum _{k=0}^n \sigma _{ik} t^k, \quad t \in [t_{i-1},t_i), \ \sigma _{ik} \in \mathbb {R}^4.\) 
